Despite the doubts floating about the crafting community (which I am a very quiet lurker) about it being tough to obtain Hearty Soft or Modena Clay, this shop on the second level of Liang Court River Valley, near to the Okonomiyaki restaurant has generous stocks of Japanese and Korean-import clay. I bought 2 bags of Grace Clay for $19.30 each, $3-$4 more expensive than what I would had purchased in Tokyu Hands for; but minus shipping costs and such, sweet deal. They also have a couple of rare clays like Silk or Angel; and they stock a large variety of cream sillicones and sauce-clays for sweets deco or food miniature making.
Apart from clay, this shop also sells cutters, molds and every other thing you would need for a clay craft hobby. However, beware their white sillicone molds are $30.00 each! Hefty price for something I paid 980 yen for. I kind of chuckled when I saw the price and decided not to burn my money into that one. Cutters are expensive too. I'll stick to my straws.
Here is the store's website : http://www.craft-it-yourself.com/about_us.html